It remains to see if our secrecy condition is equivalent to the non-signalling of [1]}, depicted in Figure REF .b.
This non-signalling corresponds roughly to secrecy under pre- and post-processing, as implemented by an initial state preparation \(f_\perp \)  and a deterministic effect \(f_\top \) .
In our picture, robustness of secrecy under pre- and post-processing is ensured by Proposition REF .
In this case, pre-processing with a function \(f_\perp \)  can be included without loss of generality in the initial state, and post-processing with \(f_\top \)  is eliminated by the choice of local perspective \(\sim _B\) .
